Democratic California Senator Dianne Feinstein won renomination, although it was unclear whether the 84-year-old would face a Republican or a Democrat in November.

California held one of the biggest primaries, with races in several other layers of government also taking place, including courts, school boards and the addition of a ballot for the mayor of San Francisco, after the unexpected death of Ed Lee in December.

Significant contests also played out elsewhere on Tuesday.

Mississippi Republican Senator Roger Wicker won his primary contest as did New Jersey Senator Bob Menendez, a Democrat who faced federal bribery charges last year. The jury deadlocked, but Republicans hope to use Menendez's legal troubles to tar other Democrats like Sherrill across the state.

Much of the day's drama focused on women, who fought to make history in some cases and to avoid disaster in others.

In Alabama, four-term Republican Republican Martha Roby was forced into a run-off election next month after failing to win 50 per cent of her party's vote. She will face former Democrat Bobby Bright in Alabama's conservative 2nd district - where Trump loyalty has been a central issue.

Roby was the first member of Congress to withdraw her endorsement of the Republican President in 2016 after he was caught on video bragging about grabbing women's genitals.

Former Miss America Mallory Hagan also won a Democratic congressional nomination in an Alabama congressional race. Hagan was crowned Miss America in 2013 and until recently worked as a news anchor in Georgia. She said she was inspired to run by the late Dr Martin Luther King jnr. She will face Mike Rogers, who is unopposed for the Republican nomination, but the deep-red district is highly unlikely to fall into Democratic hands.

Alabama Governor Kay Ivey, the state's first female governor, fended off three GOP challengers for a governor nomination, while South Dakota's Kristi Noem became the first female nominee for governor in her state as well.

In New Mexico, Democrat Michelle Lujan Grisham won her party's nomination in the race to succeed outgoing Republican Governor Susana Martinez. If Grisham wins, she'd be the state's second Latino state executive and the first Latino Democrat governor.

In Iowa, 28-year-old state Democrat Abby Finkenauer was trying to become the youngest woman to serve in Congress. And in New Mexico, former state Democratic Party chairwoman Debra Haaland, a tribal member of Laguna Pueblo, was making a bid to become the first Native American woman in Congress.

Haaland said in her primary victory statement: "Donald Trump and the billionaire class should consider this victory a warning shot: the blue wave is coming."

Much of Tuesday's focus was on California, however.

Recognising the high stakes, Trump sought to energise his supporters in a series of tweets praising his preferred California Republican candidates.

"In High Tax, High Crime California, be sure to get out and vote for Republican John Cox for Governor. He will make a BIG difference!" Trump tweeted.

Yet frightening scenarios exist for both parties.

Republican John Cox won the second spot for the California governor race ensuring the GOP won’t be shut out of the race. But the San Diego businessman faces long odds against Democrat Gavin Newsom.

Democrats, meanwhile, could be shut out of a handful of competitive House races because they ran too many primary candidates and diluted their vote.

Under California's system, all candidates appear on a single primary ballot, with the top two vote-getters regardless of party advancing to the November election. That allows the possibility of two candidates from the same party qualifying.

In the race to succeed term-limited Democrat Jerry Brown, two Democrats,  Gavin Newsom and former Los Angeles Mayor Antonio Villaraigosa, are leading the pack. For the GOP, the Trump-backed Cox, a business executive, has the best chance at earning a spot.

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It's also possible Republicans may not secure a nomination spot in the challenge against Feinstein.

On the other hand, Democrats could be shut out in a handful of House races, which would be a massive blow to the party's fight to claim the House majority this fall.

National Democrats spent more than $US7 million ($9.1 million) trying to curb and repair the damage inflicted by Democrats attacking each other in districts opened by retiring Republican Reps. Ed Royce and Darrell Issa, and the district where Republican Dana Rohrabacher was facing challenges from the left and the right.

Trump will not be on the ballot this year. But he was on the minds of many voters.

Francine Karuntzos, a 57-year-old retiree from Huntington Beach, California, said she had deep concerns about the Republican president - particularly his recent declaration that he could pardon himself. She said she wasn't a member of a political party, but she voted Democratic on Tuesday.

"I'm really, really worried about our Constitution being ruined by this presidency," Karuntzos said after casting her ballot at a local community centre.

It was a different story in Mississippi, where 66-year-old Gladys Cruz wasn't sure which Republican she would support in the state's Senate primary, but she wanted whoever won to firmly support Trump.

The President "touches my heart," she said.

Late on Wednesdaty, CNN reported that it could take days before  the results in California’s primary election are known because in Los Angeles County, "the names of 118,522 voters were left off the voter roster because of a random printing error".

AP